Problem: Simplify the following expression: $ a = 6 - \dfrac{2}{3z - 9} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3z - 9}{3z - 9}$ $ \dfrac{6}{1} \times \dfrac{3z - 9}{3z - 9} = \dfrac{18z - 54}{3z - 9} $ Therefore $ a = \dfrac{18z - 54}{3z - 9} - \dfrac{2}{3z - 9} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{18z - 54 - 2 }{3z - 9} $ Distribute the negative sign: $a = \dfrac{18z - 54 - 2}{3z - 9}$ $a = \dfrac{18z - 56}{3z - 9}$